Pythagoras's Theorem is named after Pythagoras of Samos pictured above. It is a historical debate as to who developed this theorem first, the Egyptians were using the principle and many more a long time before Pythagoras and his Pythagoreans proved it but that is a matter for others to deal with - Pythagoras has his name on it and so to him we give the credit.
There are many proofs that can show Pythagoras's Theorem:
This states that for any right angle triangle, the sum of the area of the squares on the two shorter sides (a2 + b2) will equal the area of the square on the hypotenuse (c2).
Giving the equation: a2 + b2 = c2
So if we are trying to calculate the length of any side, as long as we have the length of the other two sides, we can use pythagoras if the triangle is a right angle.
Example:
A planes flies 80 km due north and the flies 72 km due west. How far would the plane have travelled if it went there directly?
The direct of the plane has made a right angled triangle with the right angle where the plane goes from north direct to west direction. To calculate the length of the hypotenuse which is the length opposite the right angle we use the pythagoras' theorem where the hypotenuse is c.
c2 = 802 + 722
c = Squareroot( 11584)
c = 107.6 km
To find the length of one of the shorter side we would rearrange the equation and say:
The best way to see Pythagoras in 3D is interactively whether you are looking at a model or at compuet software, check out mymaths using your login details to access and you can play about to get the hang of it.
Once you've got your head around this, try some questions where you have to visualise the shapes as unfortunately you can't have a model or 3d shape in your exam.
Pythagoras of Samos - 500 BC
Pythagoras's Theorem is named after Pythagoras of Samos pictured above. It is a historical debate as to who developed this theorem first, the Egyptians were using the principle and many more a long time before Pythagoras and his Pythagoreans proved it but that is a matter for others to deal with - Pythagoras has his name on it and so to him we give the credit.
There are many proofs that can show Pythagoras's Theorem:
This states that for any right angle triangle, the sum of the area of the squares on the two shorter sides (a2 + b2) will equal the area of the square on the hypotenuse (c2).
Giving the equation: a2 + b2 = c2
So if we are trying to calculate the length of any side, as long as we have the length of the other two sides, we can use pythagoras if the triangle is a right angle.
Example:
A planes flies 80 km due north and the flies 72 km due west. How far would the plane have travelled if it went there directly?
The direct of the plane has made a right angled triangle with the right angle where the plane goes from north direct to west direction. To calculate the length of the hypotenuse which is the length opposite the right angle we use the pythagoras' theorem where the hypotenuse is c.
c2 = 802 + 722
c = Squareroot( 11584)
c = 107.6 km
To find the length of one of the shorter side we would rearrange the equation and say:
a2 = c2 - b2 where c is always the hypotenuse.
Check out some of the many proofs of this theorem at:
http://math.about.com/gi/o.htm?zi=1/XJ/Ya&zTi=1&sdn=math&cdn=education&tm=366&gps=130_511_1345_566&f=00&tt=14&bt=1&bts=1&zu=http%3A//www.ies.co.jp/math/java/geo/pythagoras.html
Pythagoras' Theorem in 3D
The best way to see Pythagoras in 3D is interactively whether you are looking at a model or at compuet software, check out mymaths using your login details to access and you can play about to get the hang of it.
http://www.mymaths.co.uk/tasks/library/loadLesson.asp?title=pythagoras/pythagoras3D
you can also try your hand at Pythagoras' who wants to be a millionaire - see if you can win the million on your own!
http://www.mymaths.co.uk/tasks/library/loadLesson.asp?title=pythagoras/pythagmillionaire
Once you've got your head around this, try some questions where you have to visualise the shapes as unfortunately you can't have a model or 3d shape in your exam.